with \(a_{ij}\)  being defined as in the above proposition.
The integral in (REF ) can be solved by resorting to partial
integration. Indeed, taking \(\log _2\left(1+c\gamma \delta \right)\)  as
the primitive factor and recalling that
\((1-\delta )^{n-m}=\sum _{\ell =0}^{n-m}{n-m \atopwithdelims ()\ell }(-1)^\ell \delta ^\ell \) ,
by virtue of [1]}, we obtain
\(&& \mathbb {E}\left[\log _2\left(1+\gamma \delta \right)\right]=\frac{K}{n}\sum _{i,j=1}^{n}a_{ij}\sum _{\ell =0}^{m-b}{m-b \atopwithdelims ()\ell }\frac{(-1)^\ell }{s_{i,j,\ell }-1}\nonumber \\&&\cdot \left[\log _2(1+c\gamma )-c\gamma \frac{{_2F_1}\left(1, s_{i,j,\ell };s_{i,j,\ell }+1;-\gamma \right)}{\ln (2)(s_{i,j,\ell })} \right]\nonumber \) 
